text: /*=========================================================================
   *
   *  Copyright NumFOCUS
   *
   *  Licensed under the Apache License, Version 2.0 (the "License");
   *  you may not use this file except in compliance with the License.
   *  You may obtain a copy of the License at
   *
   *         http://www.apache.org/licenses/LICENSE-2.0.txt
   *
   *  Unless required by applicable law or agreed to in writing, software
   *  distributed under the License is distributed on an "AS IS" BASIS,
   *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   *  See the License for the specific language governing permissions and
   *  limitations under the License.
   *
   *=========================================================================*/
  
  //  Software Guide : BeginCommandLineArgs
  //    INPUTS:  {BrainT1SliceBorder20.png}
  //    INPUTS:  {BrainProtonDensitySliceShifted13x17y.png}
  //    OUTPUTS: {ImageRegistration2Output.png}
  //    OUTPUTS: {ImageRegistration2CheckerboardBefore.png}
  //    OUTPUTS: {ImageRegistration2CheckerboardAfter.png}
  //  Software Guide : EndCommandLineArgs
  
  // Software Guide : BeginLatex
  //
  // The following simple example illustrates how multiple imaging modalities
  // can be registered using the ITK registration framework. The first
  // difference between this and previous examples is the use of the
  // \doxygen{MutualInformationImageToImageMetric} as the cost-function to be
  // optimized. The second difference is the use of the
  // \doxygen{GradientDescentOptimizer}. Due to the stochastic nature of the
  // metric computation, the values are too noisy to work successfully with the
  // \doxygen{RegularStepGradientDescentOptimizer}.  Therefore, we will use the
  // simpler GradientDescentOptimizer with a user defined learning rate.  The
  // following headers declare the basic components of this registration method.
  //
  // Software Guide : EndLatex
  
  
  // Software Guide : BeginCodeSnippet
  #include "itkImageRegistrationMethod.h"
  #include "itkTranslationTransform.h"
  #include "itkMutualInformationImageToImageMetric.h"
  #include "itkGradientDescentOptimizer.h"
  // Software Guide : EndCodeSnippet
  
  #include "itkMersenneTwisterRandomVariateGenerator.h"
  
  
  //  Software Guide : BeginLatex
  //
  //  One way to simplify the computation of the mutual information is
  //  to normalize the statistical distribution of the two input images. The
  //  \doxygen{NormalizeImageFilter} is the perfect tool for this task.
  //  It rescales the intensities of the input images in order to produce an
  //  output image with zero mean and unit variance. This filter has been
  //  discussed in Section \ref{sec:CastingImageFilters}.
  //
  //  Software Guide : EndLatex
  
  // Software Guide : BeginCodeSnippet
  #include "itkNormalizeImageFilter.h"
  // Software Guide : EndCodeSnippet
  
  //  Software Guide : BeginLatex
  //
  //  Additionally, low-pass filtering of the images to be registered will also
  //  increase robustness against noise. In this example, we will use the
  //  \doxygen{DiscreteGaussianImageFilter} for that purpose. The
  //  characteristics of this filter have been discussed in Section
  //  \ref{sec:BlurringFilters}.
  //
  //  Software Guide : EndLatex
  
  // Software Guide : BeginCodeSnippet
  #include "itkDiscreteGaussianImageFilter.h"
  // Software Guide : EndCodeSnippet
  
  
  #include "itkImageFileReader.h"
  #include "itkImageFileWriter.h"
  
  #include "itkResampleImageFilter.h"
  #include "itkCastImageFilter.h"
  #include "itkCheckerBoardImageFilter.h"
  
  
  //  The following section of code implements a Command observer
  //  that will monitor the evolution of the registration process.
  //
  #include "itkCommand.h"
  class CommandIterationUpdate : public itk::Command
  {
  public:
    using Self = CommandIterationUpdate;
    using Superclass = itk::Command;
    using Pointer = itk::SmartPointer<Self>;
    itkNewMacro(Self);
  
  protected:
    CommandIterationUpdate() = default;
  
  public:
    using OptimizerType = itk::GradientDescentOptimizer;
    using OptimizerPointer = const OptimizerType *;
  
    void
    Execute(itk::Object * caller, const itk::EventObject & event) override
    {
      Execute((const itk::Object *)caller, event);
    }
  
    void
    Execute(const itk::Object * object, const itk::EventObject & event) override
    {
      auto optimizer = static_cast<OptimizerPointer>(object);
      if (!itk::IterationEvent().CheckEvent(&event))
      {
        return;
      }
      std::cout << optimizer->GetCurrentIteration() << "   ";
      std::cout << optimizer->GetValue() << "   ";
      std::cout << optimizer->GetCurrentPosition() << std::endl;
    }
  };
  
  
  int
  main(int argc, char * argv[])
  {
    if (argc < 4)
    {
      std::cerr << "Missing Parameters " << std::endl;
      std::cerr << "Usage: " << argv[0];
      std::cerr << " fixedImageFile  movingImageFile ";
      std::cerr << "outputImagefile ";
      std::cerr << "[checkerBoardBefore] [checkerBoardAfter]" << std::endl;
      return EXIT_FAILURE;
    }
  
    // Software Guide : BeginLatex
    //
    // The moving and fixed images types should be instantiated first.
    //
    // Software Guide : EndLatex
    //
    // Software Guide : BeginCodeSnippet
    constexpr unsigned int Dimension = 2;
    using PixelType = unsigned short;
  
    using FixedImageType = itk::Image<PixelType, Dimension>;
    using MovingImageType = itk::Image<PixelType, Dimension>;
    // Software Guide : EndCodeSnippet
  
    //  Software Guide : BeginLatex
    //
    //  It is convenient to work with an internal image type because mutual
    //  information will perform better on images with a normalized statistical
    //  distribution. The fixed and moving images will be normalized and
    //  converted to this internal type.
    //
    //  Software Guide : EndLatex
  
    // Software Guide : BeginCodeSnippet
    using InternalPixelType = float;
    using InternalImageType = itk::Image<InternalPixelType, Dimension>;
    // Software Guide : EndCodeSnippet
  
  
    //  Software Guide : BeginLatex
    //
    //  The rest of the image registration components are instantiated as
    //  illustrated in Section \ref{sec:IntroductionImageRegistration} with
    //  the use of the \code{InternalImageType}.
    //
    //  Software Guide : EndLatex
  
  
    // Software Guide : BeginCodeSnippet
    using TransformType = itk::TranslationTransform<double, Dimension>;
    using OptimizerType = itk::GradientDescentOptimizer;
    using InterpolatorType =
      itk::LinearInterpolateImageFunction<InternalImageType, double>;
    using RegistrationType =
      itk::ImageRegistrationMethod<InternalImageType, InternalImageType>;
    // Software Guide : EndCodeSnippet
  
  
    //  Software Guide : BeginLatex
    //
    //  The mutual information metric type is instantiated using the image
    //  types.
    //
    //  Software Guide : EndLatex
  
    // Software Guide : BeginCodeSnippet
    using MetricType =
      itk::MutualInformationImageToImageMetric<InternalImageType,
                                               InternalImageType>;
    // Software Guide : EndCodeSnippet
  
  
    TransformType::Pointer    transform = TransformType::New();
    OptimizerType::Pointer    optimizer = OptimizerType::New();
    InterpolatorType::Pointer interpolator = InterpolatorType::New();
    RegistrationType::Pointer registration = RegistrationType::New();
  
    registration->SetOptimizer(optimizer);
    registration->SetTransform(transform);
    registration->SetInterpolator(interpolator);
  
  
    //  Software Guide : BeginLatex
    //
    //  The metric is created using the \code{New()} method and then
    //  connected to the registration object.
    //
    //  Software Guide : EndLatex
  
    // Software Guide : BeginCodeSnippet
    MetricType::Pointer metric = MetricType::New();
    registration->SetMetric(metric);
    // Software Guide : EndCodeSnippet
  
  
    //  Software Guide : BeginLatex
    //
    //  The metric requires a number of parameters to be selected, including
    //  the standard deviation of the Gaussian kernel for the fixed image
    //  density estimate, the standard deviation of the kernel for the moving
    //  image density and the number of samples use to compute the densities
    //  and entropy values. Details on the concepts behind the computation of
    //  the metric can be found in Section
    //  \ref{sec:MutualInformationMetric}.  Experience has
    //  shown that a kernel standard deviation of $0.4$ works well for images
    //  which have been normalized to a mean of zero and unit variance.  We
    //  will follow this empirical rule in this example.
    //
    //  \index{itk::Mutual\-Information\-Image\-To\-Image\-Metric!SetFixedImageStandardDeviation()}
    //  \index{itk::Mutual\-Information\-Image\-To\-Image\-Metric!SetMovingImageStandardDeviation()}
    //
    //  Software Guide : EndLatex
  
    // Software Guide : BeginCodeSnippet
    metric->SetFixedImageStandardDeviation(0.4);
    metric->SetMovingImageStandardDeviation(0.4);
    // Software Guide : EndCodeSnippet
  
    using FixedImageReaderType = itk::ImageFileReader<FixedImageType>;
    using MovingImageReaderType = itk::ImageFileReader<MovingImageType>;
  
    FixedImageReaderType::Pointer fixedImageReader =
      FixedImageReaderType::New();
    MovingImageReaderType::Pointer movingImageReader =
      MovingImageReaderType::New();
  
    fixedImageReader->SetFileName(argv[1]);
    movingImageReader->SetFileName(argv[2]);
  
  
    //  Software Guide : BeginLatex
    //
    //  The normalization filters are instantiated using the fixed and moving
    //  image types as input and the internal image type as output.
    //
    //  Software Guide : EndLatex
  
    // Software Guide : BeginCodeSnippet
    using FixedNormalizeFilterType =
      itk::NormalizeImageFilter<FixedImageType, InternalImageType>;
  
    using MovingNormalizeFilterType =
      itk::NormalizeImageFilter<MovingImageType, InternalImageType>;
  
    FixedNormalizeFilterType::Pointer fixedNormalizer =
      FixedNormalizeFilterType::New();
  
    MovingNormalizeFilterType::Pointer movingNormalizer =
      MovingNormalizeFilterType::New();
    // Software Guide : EndCodeSnippet
  
    //  Software Guide : BeginLatex
    //
    //  The blurring filters are declared using the internal image type as both
    //  the input and output types. In this example, we will set the variance
    //  for both blurring filters to $2.0$.
    //
    //  Software Guide : EndLatex
  
    // Software Guide : BeginCodeSnippet
    using GaussianFilterType =
      itk::DiscreteGaussianImageFilter<InternalImageType, InternalImageType>;
  
    GaussianFilterType::Pointer fixedSmoother = GaussianFilterType::New();
    GaussianFilterType::Pointer movingSmoother = GaussianFilterType::New();
  
    fixedSmoother->SetVariance(2.0);
    movingSmoother->SetVariance(2.0);
    // Software Guide : EndCodeSnippet
  
    //  Software Guide : BeginLatex
    //
    //  The output of the readers becomes the input to the normalization
    //  filters. The output of the normalization filters is connected as
    //  input to the blurring filters. The input to the registration method
    //  is taken from the blurring filters.
    //
    //  Software Guide : EndLatex
  
    // Software Guide : BeginCodeSnippet
    fixedNormalizer->SetInput(fixedImageReader->GetOutput());
    movingNormalizer->SetInput(movingImageReader->GetOutput());
  
    fixedSmoother->SetInput(fixedNormalizer->GetOutput());
    movingSmoother->SetInput(movingNormalizer->GetOutput());
  
    registration->SetFixedImage(fixedSmoother->GetOutput());
    registration->SetMovingImage(movingSmoother->GetOutput());
    // Software Guide : EndCodeSnippet
  
  
    fixedNormalizer->Update();
    FixedImageType::RegionType fixedImageRegion =
      fixedNormalizer->GetOutput()->GetBufferedRegion();
    registration->SetFixedImageRegion(fixedImageRegion);
  
    using ParametersType = RegistrationType::ParametersType;
    ParametersType initialParameters(transform->GetNumberOfParameters());
  
    initialParameters[0] = 0.0; // Initial offset in mm along X
    initialParameters[1] = 0.0; // Initial offset in mm along Y
  
    registration->SetInitialTransformParameters(initialParameters);
  
    //  Software Guide : BeginLatex
    //
    //  We should now define the number of spatial samples to be considered in
    //  the metric computation. Note that we were forced to postpone this
    //  setting until we had done the preprocessing of the images because the
    //  number of samples is usually defined as a fraction of the total number
    //  of pixels in the fixed image.
    //
    //  The number of spatial samples can usually be as low as $1\%$ of the
    //  total number of pixels in the fixed image. Increasing the number of
    //  samples improves the smoothness of the metric from one iteration to
    //  another and therefore helps when this metric is used in conjunction with
    //  optimizers that rely of the continuity of the metric values. The
    //  trade-off, of course, is that a larger number of samples result in
    //  longer computation times per every evaluation of the metric.
    //
    //  It has been demonstrated empirically that the number of samples is not a
    //  critical parameter for the registration process. When you start fine
    //  tuning your own registration process, you should start using high values
    //  of number of samples, for example in the range of $20\%$ to $50\%$ of
    //  the number of pixels in the fixed image. Once you have succeeded to
    //  register your images you can then reduce the number of samples
    //  progressively until you find a good compromise on the time it takes to
    //  compute one evaluation of the Metric. Note that it is not useful to have
    //  very fast evaluations of the Metric if the noise in their values results
    //  in more iterations being required by the optimizer to converge. You must
    //  then study the behavior of the metric values as the iterations progress,
    //  just as illustrated in section~\ref{sec:MonitoringImageRegistration}.
    //
    //  \index{itk::Mutual\-Information\-Image\-To\-Image\-Metric!SetNumberOfSpatialSamples()}
    //  \index{itk::Mutual\-Information\-Image\-To\-Image\-Metric!Trade-offs}
    //
    //  Software Guide : EndLatex
  
    // Software Guide : BeginCodeSnippet
    const unsigned int numberOfPixels = fixedImageRegion.GetNumberOfPixels();
  
    const auto numberOfSamples =
      static_cast<unsigned int>(numberOfPixels * 0.01);
  
    metric->SetNumberOfSpatialSamples(numberOfSamples);
    // Software Guide : EndCodeSnippet
  
  
    // For consistent results when regression testing.
    metric->ReinitializeSeed(121212);
  
    //  Software Guide : BeginLatex
    //
    //  Since larger values of mutual information indicate better matches than
    //  smaller values, we need to maximize the cost function in this example.
    //  By default the GradientDescentOptimizer class is set to minimize the
    //  value of the cost-function. It is therefore necessary to modify its
    //  default behavior by invoking the \code{MaximizeOn()} method.
    //  Additionally, we need to define the optimizer's step size using the
    //  \code{SetLearningRate()} method.
    //
    //  \index{itk::Gradient\-Descent\-Optimizer!MaximizeOn()}
    //  \index{itk::Image\-Registration\-Method!Maximize vs Minimize}
    //
    //  Software Guide : EndLatex
  
  
    // Software Guide : BeginCodeSnippet
    optimizer->SetLearningRate(15.0);
    optimizer->SetNumberOfIterations(200);
    optimizer->MaximizeOn();
    // Software Guide : EndCodeSnippet
  
  
    // Software Guide : BeginLatex
    //
    // Note that large values of the learning rate will make the optimizer
    // unstable. Small values, on the other hand, may result in the optimizer
    // needing too many iterations in order to walk to the extrema of the cost
    // function. The easy way of fine tuning this parameter is to start with
    // small values, probably in the range of $\{5.0,10.0\}$. Once the other
    // registration parameters have been tuned for producing convergence, you
    // may want to revisit the learning rate and start increasing its value
    // until you observe that the optimization becomes unstable.  The ideal
    // value for this parameter is the one that results in a minimum number of
    // iterations while still keeping a stable path on the parametric space of
    // the optimization. Keep in mind that this parameter is a multiplicative
    // factor applied on the gradient of the Metric. Therefore, its effect on
    // the optimizer step length is proportional to the Metric values
    // themselves. Metrics with large values will require you to use smaller
    // values for the learning rate in order to maintain a similar optimizer
    // behavior.
    //
    // Software Guide : EndLatex
  
    // Create the Command observer and register it with the optimizer.
    //
    CommandIterationUpdate::Pointer observer = CommandIterationUpdate::New();
    optimizer->AddObserver(itk::IterationEvent(), observer);
  
  
    try
    {
      registration->Update();
      std::cout << "Optimizer stop condition: "
                << registration->GetOptimizer()->GetStopConditionDescription()
                << std::endl;
    }
    catch (const itk::ExceptionObject & err)
    {
      std::cout << "ExceptionObject caught !" << std::endl;
      std::cout << err << std::endl;
      return EXIT_FAILURE;
    }
  
    ParametersType finalParameters = registration->GetLastTransformParameters();
  
    double TranslationAlongX = finalParameters[0];
    double TranslationAlongY = finalParameters[1];
  
    unsigned int numberOfIterations = optimizer->GetCurrentIteration();
  
    double bestValue = optimizer->GetValue();
  
  
    // Print out results
    //
    std::cout << std::endl;
    std::cout << "Result = " << std::endl;
    std::cout << " Translation X = " << TranslationAlongX << std::endl;
    std::cout << " Translation Y = " << TranslationAlongY << std::endl;
    std::cout << " Iterations    = " << numberOfIterations << std::endl;
    std::cout << " Metric value  = " << bestValue << std::endl;
    std::cout << " Numb. Samples = " << numberOfSamples << std::endl;
  
  
    //  Software Guide : BeginLatex
    //
    //  Let's execute this example over two of the images provided in
    //  \code{Examples/Data}:
    //
    //  \begin{itemize}
    //  \item \code{BrainT1SliceBorder20.png}
    //  \item \code{BrainProtonDensitySliceShifted13x17y.png}
    //  \end{itemize}
    //
    //  \begin{figure}
    //  \center
    //  \includegraphics[width=0.44\textwidth]{BrainT1SliceBorder20}
    //  \includegraphics[width=0.44\textwidth]{BrainProtonDensitySliceShifted13x17y}
    //  \itkcaption[Multi-Modality Registration Inputs]{A T1 MRI (fixed image)
    //  and a proton density MRI (moving image) are provided as input to the
    //  registration method.} \label{fig:FixedMovingImageRegistration2}
    //  \end{figure}
    //
    //  The second image is the result of intentionally translating the image
    //  \code{Brain\-Proton\-Density\-Slice\-Border20.png} by $(13,17)$
    //  millimeters. Both images have unit-spacing and are shown in Figure
    //  \ref{fig:FixedMovingImageRegistration2}. The registration is stopped at
    //  200 iterations and produces as result the parameters:
    //
    //  \begin{verbatim}
    //  Translation X = 12.9147
    //  Translation Y = 17.0871
    //  \end{verbatim}
    //  These values are approximately within one tenth of a pixel from the true
    //  misalignment introduced in the moving image.
    //
    //  Software Guide : EndLatex
  
    using ResampleFilterType =
      itk::ResampleImageFilter<MovingImageType, FixedImageType>;
  
    TransformType::Pointer finalTransform = TransformType::New();
  
    finalTransform->SetParameters(finalParameters);
    finalTransform->SetFixedParameters(transform->GetFixedParameters());
  
    ResampleFilterType::Pointer resample = ResampleFilterType::New();
  
    resample->SetTransform(finalTransform);
    resample->SetInput(movingImageReader->GetOutput());
  
    FixedImageType::Pointer fixedImage = fixedImageReader->GetOutput();
  
    resample->SetSize(fixedImage->GetLargestPossibleRegion().GetSize());
    resample->SetOutputOrigin(fixedImage->GetOrigin());
    resample->SetOutputSpacing(fixedImage->GetSpacing());
    resample->SetOutputDirection(fixedImage->GetDirection());
    resample->SetDefaultPixelValue(100);
  
  
    using OutputPixelType = unsigned char;
  
    using OutputImageType = itk::Image<OutputPixelType, Dimension>;
  
    using CastFilterType =
      itk::CastImageFilter<FixedImageType, OutputImageType>;
  
    using WriterType = itk::ImageFileWriter<OutputImageType>;
  
  
    WriterType::Pointer     writer = WriterType::New();
    CastFilterType::Pointer caster = CastFilterType::New();
  
  
    writer->SetFileName(argv[3]);
  
  
    caster->SetInput(resample->GetOutput());
    writer->SetInput(caster->GetOutput());
    writer->Update();
  
  
    // Generate checkerboards before and after registration
    //
    using CheckerBoardFilterType = itk::CheckerBoardImageFilter<FixedImageType>;
  
    CheckerBoardFilterType::Pointer checker = CheckerBoardFilterType::New();
  
    checker->SetInput1(fixedImage);
    checker->SetInput2(resample->GetOutput());
  
    caster->SetInput(checker->GetOutput());
    writer->SetInput(caster->GetOutput());
  
    // Before registration
    TransformType::Pointer identityTransform = TransformType::New();
    identityTransform->SetIdentity();
    resample->SetTransform(identityTransform);
  
    if (argc > 4)
    {
      writer->SetFileName(argv[4]);
      writer->Update();
    }
  
  
    // After registration
    resample->SetTransform(finalTransform);
    if (argc > 5)
    {
      writer->SetFileName(argv[5]);
      writer->Update();
    }
  
  
    //  Software Guide : BeginLatex
    //
    // \begin{figure}
    // \center
    // \includegraphics[width=0.32\textwidth]{ImageRegistration2Output}
    // \includegraphics[width=0.32\textwidth]{ImageRegistration2CheckerboardBefore}
    // \includegraphics[width=0.32\textwidth]{ImageRegistration2CheckerboardAfter}
    // \itkcaption[Multi-Modality Registration outputs]{Mapped moving image
    // (left) and composition of fixed and moving images before (center) and
    // after (right) registration.} \label{fig:ImageRegistration2Output}
    // \end{figure}
    //
    //  The moving image after resampling is presented on the left
    //  side of Figure \ref{fig:ImageRegistration2Output}. The center and right
    //  figures present a checkerboard composite of the fixed and
    //  moving images before and after registration.
    //
    //  Software Guide : EndLatex
  
    //  Software Guide : BeginLatex
    //
    // \begin{figure}
    // \center
    // \includegraphics[width=0.44\textwidth]{ImageRegistration2TraceTranslations}
    // \includegraphics[width=0.44\textwidth]{ImageRegistration2TraceTranslations2}
    // \itkcaption[Multi-Modality Registration plot of translations]{Sequence of
    // translations during the registration process. On the left are iterations
    // 0 to 200. On the right are iterations 150 to 200.}
    // \label{fig:ImageRegistration2TraceTranslations}
    // \end{figure}
    //
    //  Figure \ref{fig:ImageRegistration2TraceTranslations} shows the sequence
    //  of translations followed by the optimizer as it searched the parameter
    //  space. The left plot shows iterations $0$ to $200$ while the right
    //  figure zooms into iterations $150$ to $200$. The area covered by the
    //  right figure has been highlighted by a rectangle in the left image.  It
    //  can be seen that after a certain number of iterations the optimizer
    //  oscillates within one or two pixels of the true solution.  At this
    //  point it is clear that more iterations will not help. Instead it is
    //  time to modify some of the parameters of the registration process, for
    //  example, reducing the learning rate of the optimizer and continuing the
    //  registration so that smaller steps are taken.
    //
    // \begin{figure}
    // \center
    // \includegraphics[width=0.44\textwidth]{ImageRegistration2TraceMetric}
    // \includegraphics[width=0.44\textwidth]{ImageRegistration2TraceMetric2}
    // \itkcaption[Multi-Modality Registration plot of metrics]{The sequence of
    // metric values produced during the registration process. On the left are
    // iterations 0 to 200. On the right are iterations 150 to 200.}
    // \label{fig:ImageRegistration2TraceMetric}
    // \end{figure}
    //
    //  Figure \ref{fig:ImageRegistration2TraceMetric} shows the sequence of
    //  metric values computed as the optimizer searched the parameter space.
    //  The left plot shows values when iterations are extended from $0$ to
    //  $200$ while the right figure zooms into iterations $150$ to $200$.  The
    //  fluctuations in the metric value are due to the stochastic nature in
    //  which the measure is computed. At each call of \code{GetValue()}, two
    //  new sets of intensity samples are randomly taken from the image to
    //  compute the density and entropy estimates.  Even with the fluctuations,
    //  the measure initially increases overall with the number of iterations.
    //  After about 150 iterations, the metric value merely oscillates without
    //  further noticeable convergence.  The trace plots in Figure
    //  \ref{fig:ImageRegistration2TraceMetric} highlight one of the
    //  difficulties associated with this particular metric: the stochastic
    //  oscillations make it difficult to determine convergence and limit the
    //  use of more sophisticated optimization methods. As explained above,
    //  the reduction of the learning rate as the registration progresses is
    //  very important in order to get precise results.
    //
    //  This example shows the importance of tracking the evolution of the
    //  registration method in order to obtain insight into the characteristics
    //  of the particular problem at hand and the components being used.  The
    //  behavior revealed by these plots usually helps to identify possible
    //  improvements in the setup of the registration parameters.
    //
    //  The plots in Figures~\ref{fig:ImageRegistration2TraceTranslations}
    //  and~\ref{fig:ImageRegistration2TraceMetric} were generated using
    //  Gnuplot\footnote{\url{http://www.gnuplot.info/}}.  The scripts used for
    //  this purpose are available in the \code{ITKSoftwareGuide} Git repository
    //  under the directory
    //
    //  ~\code{ITKSoftwareGuide/SoftwareGuide/Art}.
    //
    //  Data for the plots was taken directly from the output that the
    //  Command/Observer in this example prints out to the console. The output
    //  was processed with the UNIX editor
    //  \code{sed}\footnote{\url{http://www.gnu.org/software/sed/sed.html}} in
    //  order to remove commas and brackets that were confusing for Gnuplot's
    //  parser. Both the shell script for running \code{sed} and for running
    //  {Gnuplot} are available in the directory indicated above. You may find
    //  useful to run them in order to verify the results presented here, and to
    //  eventually modify them for profiling your own registrations.
    //
    //  \index{Open Science}
    //
    //  Open Science is not just an abstract concept. Open Science is something
    //  to be practiced every day with the simple gesture of sharing information
    //  with your peers, and by providing all the tools that they need for
    //  replicating the results that you are reporting. In Open Science, the
    //  only bad results are those that can not be
    //  replicated\footnote{\url{http://science.creativecommons.org/}}. Science
    //  is dead when people blindly trust authorities~\footnote{For example:
    //  Reviewers of Scientific Journals.} instead of verifying their statements
    //  by performing their own experiments ~\cite{Popper1971,Popper2002}.
    //
    //  Software Guide : EndLatex
  
    return EXIT_SUCCESS;
  }
  